Holt McDougal Algebra 1
2-7 Rates, Ratios, and Proportions
Bellringer: Solve each equation.
1. |x| = -19
2. Marc makes $80.50 for working 8 hours. What is his
hourly rate?
3. 2|x + 1| = 20
4.
No Solutions
5 y 2 10
Marc makes $10.06 per hour
y = 25=
x = -11, 9
Holt McDougal Algebra 1
2-7 Rates, Ratios, and Proportions2-7 Rates, Ratios, and Proportions
Holt Algebra 1
•BellringerBellringer
•Review Day: Quiz TOMORROWReview Day: Quiz TOMORROW
•Proportions, rates, ratiosProportions, rates, ratios
•Evaluating Absolute Value Evaluating Absolute Value
•Evaluating multi-step EquationsEvaluating multi-step Equations
Holt McDougal Algebra 1
Holt McDougal Algebra 1
2-7 Rates, Ratios, and Proportions
Students will be ready to ace the quiz tomorrow morning!
Objectives
Holt McDougal Algebra 1
2-7 Rates, Ratios, and Proportions
What is this called? 4: 9
What is another way to write 4:9?
Ratio
4 9
Holt McDougal Algebra 1
2-7 Rates, Ratios, and Proportions
In the proportion , the products a • d and
b • c are called cross products. You can solve
a proportion for a missing value by using the
Cross Products property.
Cross Products Property
WORDS NUMBERS ALGEBRA
In a proportion, cross products are equal.
2 • 6 = 3 • 4
If and b ≠ 0
and d ≠ 0then ad = bc.
Holt McDougal Algebra 1
2-7 Rates, Ratios, and Proportions
Example 4: Solving Proportions
Solve each proportion.
3(m) = 5(9)
3m = 45
m = 15
Use cross products.
Divide both sides by 3.
Use cross products.
6(7) = 2(y – 3)
42 = 2y – 6+6 +648 = 2y
24 = y
A. B.
Add 6 to both sides.Divide both sides by 2.
Holt McDougal Algebra 1
2-7 Rates, Ratios, and Proportions
Check It Out! Example 4
Solve each proportion.
y = −20
–12 –124g = 23
g = 5.75
A. B.
Use cross products.
Divide both sides by 2.
Use cross products.
Subtract 12 from both sides.
Divide both sides by 4.
2y = –40
2(y) = –5(8) 4(g +3) = 5(7)
4g +12 = 35
Holt McDougal Algebra 1
2-7 Rates, Ratios, and Proportions
More examples…
• 3 gallons of paint cover 200 square feet. How many gallons will cover 300 square feet?
3 x200 300
=
900 = 200x 4.5 = x
4.5 gallons of paint will cover 300 square feet.
Holt McDougal Algebra 1
2-7 Rates, Ratios, and Proportions
More examples…
• Making 5 apple pies requires 2 pounds of apples. How many pounds of apples are needed to make 18 pies?
5 18 2 x
=
36 = 5x7.2 = x
7.2 pounds of apples are need to make 8 pies
Holt McDougal Algebra 1
2-7 Rates, Ratios, and Proportions
More examples…
• Tony can run 10 blocks in 4 minutes. How long does it take him to run 15 blocks, at the same speed.
10 20 4 x
=
80 = 10x8 = x
It will take Tony 8 minutes to run 15 blocks
Holt McDougal Algebra 1
2-7 Rates, Ratios, and Proportions
Check It Out! Example 2
Cory earns $89.50 in 8 hours. Find the unit rate.
The unit rate is $11.19 per hour.
-Cory earns $11.19 per hour.
89.5 = 8x
89.5 x 8 1
=
11.19 = x
Holt McDougal Algebra 1
2-7 Rates, Ratios, and Proportions
The ratio of games won to games lost for the Miami Heat basketball team is 3:2. The team has won 18 games. How many games did the team lose?
Check It Out! Example 1
The team lost 12 games.
Holt McDougal Algebra 1
2-7 Rates, Ratios, and Proportions
Example 2: Finding Unit Rates
Raulf Laue of Germany flipped a pancake 416 times in 120 seconds to set the world record. Find the unit rate. Round your answer to the nearest hundredth.
The unit rate is about 3.47 flips/s.
Holt McDougal Algebra 1
2-7 Rates, Ratios, and Proportions
Check It Out! Example 2
Cory earns $52.50 in 7 hours. Find the unit rate.
The unit rate is $7.50.
Write a proportion to find an equivalent ratio with a second quantity of 1.
Divide on the left side to find x.7.5 = x
Holt McDougal Algebra 1
2-7 Rates, Ratios, and Proportions
Example 5A: Scale Drawings and Scale Models
A contractor has a blueprint for a house drawn to the scale 1 in: 3 ft.
A wall on the blueprint is 6.5 inches long. How long is the actual wall?
blueprint 1 in. actual 3 ft.
x • 1 = 3(6.5)
x = 19.5The actual length of the wall is 19.5 feet.
Write the scale as a fraction.
Let x be the actual length.
Use the cross products to solve.
Holt McDougal Algebra 1
2-7 Rates, Ratios, and Proportions
Past Review
Solve for x.
5x – 8 = 32+ 8 + 8
5x = 40
x = 8 (Divide by 5)
Holt McDougal Algebra 1
2-7 Rates, Ratios, and Proportions
Past Review…
• Solve for x.
4x – 6x + 8 = -4-2x + 8 = -4
- 8 - 8
-2x = -12
x = 6 (Divide by -2)
Holt McDougal Algebra 1
2-7 Rates, Ratios, and Proportions
More Word Problems…
1. In a school, the ratio of boys to girls is 4:3. There are 216 boys. How many girls are there?162
2. Nuts cost $10.75 for 3 pounds. Find the unit rate in dollars per pound. $3.58/lb
3.
4. A scale model of a car is 9 inches long. The scale is 1:18. How many inches long is the car it represents?
16
162 in.
Holt McDougal Algebra 1
2-7 Rates, Ratios, and Proportions
- Review Worksheet
- Ask any questions you have about the quiz now! It will be our largest quiz so far.
Top Related